Does the soul of the father remain suspended until the debt resulting from a car purchase transaction in his name is paid off, knowing that the son is the one who pays the installments and is unable to pay the full amount at once?

If the car was bought in your deceased father's name because he was an employee, but you were the one who paid its price, then the car is yours and the debt is upon you, not upon your father. Bank financing for car purchases is permissible if the bank buys the car and then sells it to you in installments (murabaha). However, if the bank gives you its price with an increase, it is a usurious and forbidden loan. If the purchase was made in a forbidden manner, the car is yours, and you are permitted to benefit from it, provided you repent and expedite the repayment.